Linear Modeling of AR Processes and Power Spectrum Estimation: Yule-Walker, Covariance, Burg, and Modified Covariance Methods

In linear modeling of AR processes and power spectrum estimation, several commonly used methods are available, including the Yule-Walker method (also known as the autocorrelation method), covariance method, Burg method, and modified covariance method. Each approach has distinct advantages and specific application scenarios.

The Yule-Walker method (autocorrelation method) estimates AR model parameters using sample autocorrelation function values. This method is particularly effective for signals with strong autocorrelation properties. In MATLAB implementation, this can be achieved using the aryule function, which solves the Yule-Walker equations through Levinson-Durbin recursion for efficient computation of autoregressive parameters.

The covariance method employs sample covariance matrix computation, where eigenvalues and eigenvectors are analyzed to derive AR model parameter estimates. This approach is suitable for signals exhibiting strong linear correlation characteristics. Code implementation typically involves constructing a covariance matrix from signal segments and applying eigenvalue decomposition techniques.

The Burg method operates on the principle of minimizing mean-square error criteria, utilizing iterative procedures to progressively estimate AR model parameters. This technique is optimal for signals with pronounced autoregressive properties. The arburg function in MATLAB implements this method using lattice filter structures and forward-backward prediction error minimization.

The modified covariance method enhances standard covariance estimation by incorporating correction factors to reduce estimation bias, particularly beneficial when working with limited sample sizes and strongly correlated signals. Implementation often involves modified matrix formulations with regularization parameters to improve numerical stability.

Therefore, when performing linear modeling and power spectrum estimation for AR processes, appropriate method selection based on specific signal characteristics ensures accurate parameter estimation results.